Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet. a. Find the length of the side of the lot opposite the 60° angle. b. Find the length of the hypotenuse of the triangular lot. c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

Answer 1

OK, do you know the ratios of a 30-60-90 triangle?

Answer 2

No. I have no clue.

Answer 3

Seen something with 1/2, 1, and the square root of 3 over 2? Or they may do 1, 2, and the square root of 3.

Answer 4

I'm not sure. I din't learn about this in the lesson.

Answer 5

They probably expect you to rememebr it from some prior math.
http://commons.wikimedia.org/wiki/File:30-60-90_triangle.jpg

That is the set ratio for a 30-60-90. EVERY 30-60-90 uses that ratio.

Answer 6

In your case, they say "The side opposite the 30° angle measures 41 feet." So, what would be 41?

Answer 7

a=41?

Answer 8

Exactly! Now, if a=41, can you solve the other sides they ask for?

Answer 9

2a=82.

Answer 10

Yes, so which side is the 82?

Answer 11

a*sqrt3=71.01408.?

Answer 12

Yah, that is the root one. And which questions to they answer? You have the numbers right. Just make sure to get them in the right places!

Answer 13

So the answer to Find the length of the side of the lot opposite the 60° angle is 71.01408?

Answer 14

And the answer to Find the length of the hypotenuse of the triangular lot is 82 ft?

Answer 15

/cheer

Answer 16

Exactly. So all that is left is the trig ratios based on those values.

Answer 17

Should I round 71.01408 off?

Answer 18

"Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places." do the calculation first, then round to 4 as stated.

Answer 19

If you round first, then calculate, it has a greater chance of error. If you do the ratio first, then round, you should get the answer they want.

Answer 20

How do I find the sine, cosine, and tangent? I haven't done this in so long!

Answer 21

Can I just punch in on a calculator sin 30? Tan 30?

Answer 22

Well, that might work... but they mean the SOH CAH TOA ratios, from the way they stated it.

Answer 23

SOH CAH TOA, a mnemonic pronounced Soh Kah Toah (or something like that) which stands for:\[S=\frac{O}{H},~C=\frac{A}{H},~T=\frac{O}{A}\\
\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}},~\cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}},~\tan\theta=\frac{\text{Opposite}}{\text{Adjacent}}\]

Answer 24

Sin=41/82?

Answer 25

Cos=71/82?

Answer 26

Well, 71.whatever, but yah

Answer 27

Sin=0.5.....rounded four places would be 0.9?

Answer 28

Cosine=0.8660......Rounded four places would be 0.8664?

Answer 29

0.86602536585365853658536585365854
The fourth place is 0. The 5th is 2. So
0.8660

Answer 30

And .5 rounded to 4 places is .5000 or just .5.

Answer 31

Okay. Tangent=41/?

Answer 32

41/71.01408

Answer 33

0.5773502944768136121738111653351 So what would that round to?

Answer 34

0.5773?

Answer 35

Well, 5 is the border. Typically it rounds up at that point.

Answer 36

<5 on the next decimal, round down. >=5, round up.
0.57735 has a 5 at the end, so round up.
0.5774

Answer 37

Thank you!

Answer 38

np. Don't have too much fun. And yah, math is progressive so they expect you to remember everything you did before.